Renewable energy sources (RES) and HVDC links are typically interfaced with the grid by power converters, whose performance during grid faults is significantly different from that of traditional synchronous generators. This paper investigates the performance of grid-connected voltage source converters (VSCs) under unbalanced faults. Conventional positive-sequence synchronous reference frame (SRF) control is presented first, followed by three different negative-sequence current control strategies considering reactive power injection and converter current limit. The simulation results indicate that the performance of VSCs varies with their control strategies. Negative-sequence current control is necessary to restrict converter current in each phase under unbalanced faults. Among presented control strategies, the balanced current control strategy complies with the present voltage support requirement best and further requirements should be specified if a set of controlled unbalanced current is expected under unbalanced faults.